具时滞和Holling功能性反应的捕食-被捕食系统的稳定性及Hopf分支  

The stability and Hopf bifurcation of a predator-prey system with time delay and Holling type functional response function

作　　者：郭坤[1] 潘家齐[2] 

机构地区：[1]东北师范大学商学院,吉林长春130117 [2]东北师范大学数学与统计学院,吉林长春130024

出　　处：《黑龙江大学自然科学学报》2006年第4期502-505,共4页Journal of Natural Science of Heilongjiang University

摘　　要：以滞量为参数,研究一类具时滞和Holling型功能性反应函数的捕食———被捕食系统正平衡点的稳定性和Hopf分支.发现对于滞量τ,系统存在稳定性开关,即当τ变化经过某些值时,系统的正平衡点的稳定性发生变化,即从渐近稳定到不稳定,再到渐近稳定,经过有限次这样的循环,最后进入不稳定状态.而且这些τ值是系统的Hopf分支值.并在第一个分支点τ0给出Hopf分支分析.Consider the stability and bifurcation of positive equilibrium for a predator - prey model with a delay argument and Holling type functional response function. It is shown for some delay T,the system exists stability switch, it means that, when T undergoes some values, the stability of positive eqilibrium alters, it changes from asymptotical steadiness to unsteadiness, and then turns aside. After such a finite cycling, at last it will turn into an unsteady state. These values of T are Hopf bifurcation values of the system. The analysis of Hopf bifurcation is given at the first critical value To.

关 键 词：Holling型功能性反应函数 捕食-被捕食系统 时滞 HOPF分支 稳定性 

分 类 号：O175.14[理学—数学]